UIUC Dept. of Mathematics Seminar Calendar

      March 2003             April 2003              May 2003      
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Thursday, April 10, 2003

Number Theory Seminar
1:00 pm in 241 Altgeld Hall, Thursday, April 10, 2003

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Submitted by ford.

Frank Garvan (University of Florida Math.)
Relations between the ranks and cranks of partitions
Abstract: ew identities and congruences involving the ranks and cranks of partitions are proved. The proof depends on a new partial differential equation connecting their generating functions. This is recent joint work with A.O.L. Atkin.

Group Theory Seminar
1:00 pm in Altgeld Hall room 347, Thursday, April 10, 2003

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Submitted by kapovitc.

Ilya Kapovich (UIUC Math)
Genericity for Whitehead's algorithm, for stabilizers in Aut(F) and for one-relator groups
Abstract: We use a combination of algebraic and probabilistic methods (in particular Large Deviation Theory) to show that the classical algorithm of Whitehead for solving the automorphic equivalence problem in a finitely generated free group F works in linear time. on an exponentially generic set of inputs. Moreover, it turns out that a generic element of F has trivial stabilizer in Out(F). Our results also imply that generic one-relator groups are complete, that is, they have trivial centers and trivial outer automorphism groups. Even the fact that complete one-relator groups exist is new, and we establish their existence by a classical probabilistic argument, that is, by proving that a randomly chosen one-relator group is complete with "positive probability". Moreover, we are able to compute the precise asymptotics of the number of isomorphism types of k-generator one-relator groups when the length of the defining relator goes to infinity.

Probability and Statistics Seminar
4:00 pm in 2 Illini Hall, Thursday, April 10, 2003

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Rong Chen (Professor, University of Illinois - Chicago)
Sequential Monte Carlo and its application in protein structure analysis
Abstract: Stochastic systems are routinely used in science, engineering and economics. Many of these systems have a natural dynamic structure; others can often be built up dynamically. Sequential Monte Carlo (SMC) can be loosely defined as a family of methodologies that use Monte Carlo simulation to solve estimation and prediction problems in dynamic systems. By recursively generating Monte Carlo samples of the state variables or some other latent variables, these methods can easily adapt to the dynamics of the underlying stochastic systems. In this talk we first briefly review the basic framework of SMC. Then we discuss how it can be applied to study the geometric properties of chain polymer, a simple model for protein structure.